Question

Find dy/dx for the given value of x y=2 root x(3x-2); x=4

Answer 1

Answer:

For parametric form of equation,

d

y

d

x

=

d

y

d

t

d

x

d

t

.

Here as

x

=

t

2

−

2

t

,

d

x

d

t

=

2

t

−

2

=

2

(

t

−

1

)

and as

y

=

t

4

−

4

t

,

d

y

d

t

=

4

t

3

−

4

=

4

(

t

3

−

1

)

=

4

(

t

−

1

)

(

t

2

+

t

+

1

)

Hence

d

y

d

x

=

4

(

t

−

1

)

(

t

2

+

t

+

1

)

2

(

t

−

1

)

=

2

(

t

2

+

t

+

1

)